Cayley hamilton theorem: Cayley-Hamilton theorem by Marco Taboga

Cayley-Hamilton theorem by Marco Taboga, PhD The Cayley-Hamilton theorem shows that the characteristic polynomial of a square matrix is identically equal to zero when it is transformed into a polynomial in the matrix itself. In other words, a square matrix satisfies its own characteristic equation. Theorem 1.3.1 Every square matrix satisfies its characteristic equation Cayley-Hamilton theorem has two important uses (1) to find the inverse of a non-singular matrix A and (2) to find higher integral powers of A. Learn the Cayley Hamilton Theorem with a clear statement, step-by-step proof, essential formulas, and solved examples. Understand how matrices satisfy their own characteristic equations. In linear algebra, the Cayley–Hamilton theorem (termed after the mathematicians Arthur Cayley and William Rowan Hamilton) says that every square matrix over a commutative ring (for instance the real or complex field) satisfies its own characteristic equation.